When a putter head hits a golf ball, the putter exerts a force on the ball, and the ball exerts an equal force on the putter in the opposite direction. In general, the force exerted on the putter by the ball does two things. It slows down the forward linear motion of the putter, and it causes the putter head to rotate about the vertical axis through its center of mass (COM).
This rotation of the putter head is undesirable because it produces an error in the direction and speed of the ball. If the face of the incident head is perpendicular to the desired initial direction of the ball, as it should be, then the error arises because the rotated head will point away from this desired direction. During the brief time that the ball is in contact with the face of the putter head, the putter head will have rotated through a small angle so that, when the ball leaves the face of the putter head, it will move in a direction which is approximately perpendicular to the rotated face instead of the direction perpendicular to the original face. Also, because some of the kinetic energy of the incident putter head goes into the rotational energy acquired by the putter head, the speed of the struck ball will be less than anticipated.
However, if ball is hit directly in front of the COM of the putter head, then there will be no induced rotation about the COM axis, and the above direction and speed errors will be avoided. Of course, the ball is not often hit directly in front of the COM of the putter head. Thus, the moment of inertia (MOI) of the putter head about the vertical axis through the COM of the putter head is important. (This MOI is defined as Σmiri2, where each mass element mi is multiplied by the square of the perpendicular distance ri between the position of the element and the chosen vertical axis that intersects the COM of the putter head.) For an impact that is not directly in front of the COM of the putter head, the larger the MOI, the smaller the angular error. In other words, the larger the MOI, the larger the area on the clubface that produces an acceptable hit. This relationship is why the MOI is so important.
USGA regulations restrict the size of a putter head, but not the weight or MOI of the putter head. Professional golfers consistently hit the ball very close to the point on the putter face directly in front of the COM of the putter head. This point may be referred to as the COM-point or “sweet spot” on the face of the putter head.
Many articles, books, and patents erroneously claim that the sweet spot is the point in front of the center of percussion (COP) of the putter head. The confusion arises because the COP of the putter head is the point where an impact does not induce a reaction at the shaft insertion point into the putter head. An impact at the COP of the putter head, therefore, does not eliminate a putter head rotation, but instead creates a rotation about the COM of the putter head, since this created rotation must cancel the translational motion at the shaft induced by the impact. This rotation causes the ball to leave the clubface in the wrong direction. The sweet spot of the head is therefore the COM, not the COP, of the putter head.
Amateur golfers, on the other hand, usually hit the ball at a point on the clubface that is a fair distance (often 0.5″ and sometimes over 1″) from the COM point of the putter head. It is, therefore, in the interest of most golfers to use a club with as large a MOI as possible.